To determine the sum of the expressions [tex]\(-2x + 7x + 1\)[/tex] and [tex]\(-3x - 7\)[/tex], follow these steps:
1. Combine the Like Terms:
First, let's identify the like terms in each expression. The like terms are the terms that contain the variable [tex]\(x\)[/tex]:
[tex]\[
-2x + 7x \quad \text{and} \quad -3x
\][/tex]
Now, combine these like terms:
[tex]\[
(-2x + 7x) + (-3x) = (5x) + (-3x) = 5x - 3x = 2x
\][/tex]
2. Combine the Constants:
Next, look at the constant terms from the expressions [tex]\(1\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[
+1 \quad \text{and} \quad -7
\][/tex]
Combining these constants:
[tex]\[
1 - 7 = -6
\][/tex]
3. Construct the Final Expression:
After combining the like terms and the constants, we can now construct the final expression:
[tex]\[
2x - 6
\][/tex]
So, the sum of [tex]\(-2x + 7x + 1\)[/tex] and [tex]\(-3x - 7\)[/tex] is:
[tex]\[
2x - 6
\][/tex]
